Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

Characterisation and environmental application of an Australian natural zeolite for basic dye removal from aqueous solution

An Australian natural zeolite was collected, characterised and employed for basic dye adsorption in aqueous solution. The natural zeolite is mainly composed of clinoptiloite, quartz and mordenite and has cation-exchange capacity of 120 meq/100 g. The natural zeolite presents higher adsorption capacity for methylene blue than rhodamine B with the maximal adsorption capacity of 2.8 x 10(-5) and 7.9 x 10(-5) Mot/g at 50 degrees C for rhodamine B and methylene blue, respectively. Kinetic studies indicated that the adsorption followed the pseudo second-order kinetics and could be described as two-stage diffusion process. The adsorption isotherm could be fitted by the Langmuir and Freundlich models. Thermodynamic calculations showed that the adsorption is endothermic process with Delta H degrees at 2.0 and 8.7 kJ/mol for rhodamine B and methylene blue. It has also found that the regenerated zeolites by high-temperature calcination and Fenton oxidation showed similar adsorption capacity but lower than the fresh sample. Only 60% capacity could be recovered by the two regeneration techniques. (c) 2006 Elsevier B.V. All rights reserved.

Coal ash conversion into effective adsorbents for removal of heavy metals and dyes from wastewater

Fly ash was modified by hydrothermal treatment using NaOH solutions under various conditions for zeolite synthesis. The XRD patterns are presented. The results indicated that the samples obtained after treatment are much different. The XRD profiles revealed a number of new reflexes, suggesting a phase transformation probably occurred. Both heat treatment and chemical treatment increased the surface area and pore volume. It was found that zeolite P would be formed at the conditions of higher NaOH concentration and temperature. The treated fly ash was tested for adsorption of heavy metal ions and dyes in aqueous solution. It was shown that fly ash and the modified forms could effectively absorb heavy metals and methylene blue but not effectively adsorb rhodamine B. Modifying fly ash with NaOH solution would significantly enhance the adsorption capacity depending on the treatment temperature, time, and base concentration. The adsorption capacity of methylene blue would increases with pH of the dye solution and the sorption capacity of FA-NaOH could reach 5 x 10(-5) mol/g. The adsorption isotherm could be described by the Langmuir and Freundlich isotherm equations. Removal of copper and nickel ions could also be achieved on those treated fly ash. The removal efficiency for copper and nickel ions could be from 30% to 90% depending on the initial concentrations. The increase in adsorption temperature will enhance the adsorption efficiency for both heavy metals. The pseudo second-order kinetics would be better for fitting the dynamic adsorption of Cu and Ni ions. (c) 2005 Elsevier B.V. All rights reserved.

Adsorption kinetics for the removal of chromium(VI) from aqueous solution by adsorbents derived from used tyres and sawdust

The batch removal of hexavalent chromium (Cr(Vl)) from wastewater under different experimental conditions using economic adsorbents was investigated in this study. These adsorbents were produced from the pyrolysis and activation of the waste tyres (TAC) and from the pyrolysis of sawdust (SPC). The performance of these adsorbents against commercial activated carbon F400 (CAC) has also been carried out. The removal was favoured at low pH, with maximum removal at pH = 2 for all types of carbon. The effects of concentration, temperature and particle size have been reported. All sorbents were found to efficiently remove Cr(VI) from solution. The batch sorption kinetics have been tested for a first-order reversible reaction, a first-order and second-order reaction. The rate constants of adsorption for all these kinetic models have been calculated. The applicability of the Langmuir isotherm for the present system has been tested at different temperatures. The thermodynamic parameters (AGO, K,) obtained indicate the endothermic nature of Cr(Vl) adsorption on TAC, SPC and CAC. (C) 2001 Elsevier Science B.V. All rights reserved.

Adsorption study for removal of basic red dye using bentonite

Colored wastewater poses a challenge to the conventional wastewater treatment techniques. Solid-liquid phase adsorption has been found to be effective for the removal of dyes from effluent. In this paper, the ability of bentonite as an adsorbent for the removal of a commercial dye, Basic Red 2 (BR2), from an aqueous solution has been investigated under various experimental conditions. The adsorption kinetics was shown to be pseudo-second-order. It was found that bentonite had high adsorption capacity for BR2 due to cation exchange. The adsorption equilibrium data can be fitted well by the Langmuir adsorption isotherm model. The effect of the experimental parameters, such as temperature, salt, and pH was investigated through a number of batch adsorption experiments. It was found that the removal of dye increased with the increase in solution pH. However, the change of temperature (15-45 degrees C) and the addition of sodium chloride were found to have little effect on the adsorption process. The results show that electrostatic interactions are not dominant in the interaction between BR2 and bentonite. It was found that the adsorption was a rapid process with 80-90% of the dye removed within the first 2-3 min. Bentonite as an adsorbent is promising for color removal from wastewater.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

A kinetic study of the thermally initiated free radical reactions of styrene with octanedithiol as a model for the reactions of multifunctional thiols with divinylbenzene

The kinetics of chain reactions of octanedithiol with styrene, thermally initiated with TX29B50 (a 50:50 wt% solution of TX29 diperoxy initiator in a phthalate plasticizer), have been studied over a range of initiator concentrations, a range of mixture formulations and a range of temperatures. This system has been investigated as a model system for the reactions of polyfunctional thiols with divinyl benzene. The reactions have been shown to follow first-order kinetics for both the thiol and the ene species and to be characterized by a dependence on the initiator concentration to the power of one half. The kinetic rate parameters have been shown to adhere to Arrhenius behaviour. A kinetic model for the chain reactions for this system has been proposed. (C) 2003 Society of Chemical Industry.

The physical and surface chemical characteristics of activated carbons and the adsorption of methylene blue from wastewater

Adsorption of a basic dye, methylene blue, from aqueous solutions onto as-received activated carbons and acid-treated carbons was investigated. The physical and surface chemical properties of the activated carbons were characterized using BET-N-2 adsorption, X-ray photoelectron spectroscopy (XPS), and mass titration. It was found that acid treatment had little effect on carbon textural characteristics but significantly changed the surface chemical properties, resulting in an adverse effect on dye adsorption. The physical properties of activated carbon, such as surface area and pore volume, have little effect on dye adsorption, while the pore size distribution and the surface chemical characteristics play important roles in dye adsorption. The pH value of the solution also influences the adsorption capacity significantly. For methylene blue, a higher pH of solution favors the adsorption capacity. The kinetic adsorption of methylene blue on all carbons follows a pseudo-second-order equation. (c) 2004 Elsevier Inc. All rights reserved.

The BeWo choriocarcinoma cell line as a model of iodide transport by placenta

Cultured human choriocarcinoma cells of the BeWo line exhibited saturable accumulation of radioiodide. Inhibition by competing anions followed the affinity series perchlorate >= iodide >= thiocyanate, consistent with uptake through the thyroid iodide transporter, NIS, whose messenger RNA was found in BeWo cells, and whose protein was distributed towards the apical pole of the cells. Efflux obeyed first order kinetics and was inhibited by DIDS, an antagonist of anion exchangers including pendrin, whose messenger RNA was also present. In cultures where iodide uptake through NIS was blocked with excess perchlorate, radiolodide accumulation was stimulated by exposure to medium in which physiological anions were replaced by 2-morpholinoethanesulfonic acid (MES), consistent with the operation of an anion exchange mechanism taking up iodide. Chloride in the medium was more effective than sulfate at inhibiting this uptake, matching the ionic specificity of pendrin. These studies provide evidence that the trophoblast accumulates iodide through NIS and releases it to the fetal compartment through pendrin. (c) 2004 Elsevier Ltd. All rights reserved.

Gypsum solubility in seawater, and its application to bauxite residue amelioration

The solubilities and dissolution rates of three gypsum sources (analytical grade (AG), phosphogypsum (PG) and mined gypsum (MG)) with six MG size fractions ((mm) > 2.0, 1.0-2.0, 0.5-1.0, 0.25-0.5, 0.125-0.25, and < 0.125) were investigated in triple deionised water (TDI) and seawater to examine their suitability for bauxite residue amelioration. Gypsum solubility was greater in seawater (3.8 g L 1) than TDI (2.9 g L 1) due to the ionic strength effect, with dissolution in both TDI and seawater following first order kinetics. Dissolution rate constants varied with gypsum source (AR > PG > MG) due to reactivity and surface area differences, with 1:20 gypsum:solution suspensions reaching saturation within 15 s (AR) to 30 min (MG > 2.0). The ability of bauxite residue to adsorb Ca from solution was also examined. The quantity of the total solution Ca adsorbed was found to be small (5 %). These low rates of solution Ca adsorption combined with the comparatively rapid dissolution rates preclude the application of gypsum to the residue sand/seawater slurry as a method for residue amelioration. Instead, direct field application to the residue would ensure more efficient gypsum use. In addition, the formation of a sparingly soluble CaCO3 coating around the gypsum particles after mixing in a highly alkaline seawater/supernatant liquor (SNL) solution greatly reduced the rate of gypsum dissolution.

Metabolite mean transit times in the liver as predicted by various models of hepatic elimination

Predicted area under curve (AUC), mean transit time (MTT) and normalized variance (CV2) data have been compared for parent compound and generated metabolite following an impulse input into the liver, Models studied were the well-stirred (tank) model, tube model, a distributed tube model, dispersion model (Danckwerts and mixed boundary conditions) and tanks-in-series model. It is well known that discrimination between models for a parent solute is greatest when the parent solute is highly extracted by the liver. With the metabolite, greatest model differences for MTT and CV2 occur when parent solute is poorly extracted. In all cases the predictions of the distributed tube, dispersion, and tasks-in-series models are between the predictions of the rank and tube models. The dispersion model with mixed boundary conditions yields identical predictions to those for the distributed tube model (assuming an inverse gaussian distribution of tube transit times). The dispersion model with Danckwerts boundary conditions and the tanks-in series models give similar predictions to the dispersion (mixed boundary conditions) and the distributed tube. The normalized variance for parent compound is dependent upon hepatocyte permeability only within a distinct range of permeability values. This range is similar for each model but the order of magnitude predicted for normalized variance is model dependent. Only for a one-compartment system is the MIT for generated metabolite equal to the sum of MTTs for the parent compound and preformed metabolite administered as parent.